Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y - 3 = 8/3 * (x + 2) (- 2, 3)
(1 point)
To find the equation of a line perpendicular to the given line, we first need to find the slope of the given line. We can observe that the given line is in slope-intercept form (y = mx + b) with a slope of 8/3.
The formula for finding the slope of perpendicular lines is: m(perpendicular) = -1/m(original)
Applying the formula, we find the slope of the perpendicular line:
m(perpendicular) = -1/(8/3) = -3/8
Now, to find the equation of the perpendicular line passing through the given point (-2, 3), we can use the point-slope form of a line:
y - y1 = m(x - x1)
Plugging in the values:
y - 3 = (-3/8) * (x - (-2))
Simplifying:
y - 3 = (-3/8) * (x + 2)
Thus, the equation of the line that is perpendicular to y - 3 = 8/3 * (x + 2) and passes through (-2, 3) is y - 3 = (-3/8) * (x + 2).
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -113. Can you be confident that your predicted value wd be reasonably close to the actual value? Why or why not?
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no linear correlation.
In this case, the correlation coefficient is -113, which is not a valid value for the correlation coefficient. The correlation coefficient cannot be less than -1 or greater than +1.
Therefore, based on this information, it is not possible to determine whether the predicted value will be reasonably close to the actual value. The invalid correlation coefficient suggests that there may be an error or mistake in the calculation or interpretation of the data. Further investigation and correction are needed before making any confident predictions.
To find the equation of a line that is perpendicular to the given line and passes through the given point, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line is in the form y - y1 = m(x - x1), where (x1, y1) represents a point on the line, and m is the slope. So, the given line can be rewritten as:
y - 3 = (8/3)(x + 2)
To find the slope, we can compare the equation to the standard slope-intercept form (y = mx + b), where m represents the slope. From the given equation, we can see that the slope is 8/3.
The negative reciprocal of 8/3 is -3/8. So, the slope of the line perpendicular to the given line is -3/8.
Now we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) represents the given point and m is the slope.
Using the point (-2, 3) and the slope -3/8, we get:
y - 3 = (-3/8)(x + 2)
This is the equation of the line that is perpendicular to the given line and passes through the given point.